please help me solving following integration.......

Question

anonymous · Answer

And the solution is

hartnn · Answer

we can't help u unless u post the question.

anonymous · Answer

$$\frac{ 1 }{ a+iw}\times \frac{ 1 }{ b+iw }\times e ^{iwt}$$

lgbasallote · Answer

i wonder if September is the season of integrals....i see so many calc questions

anonymous · Answer

this is the to be integrated...

lgbasallote · Answer

wait...how is that integration? did i miss the meaning of the integration? doesnt integration have $\int$ thingies?

anonymous · Answer

with respect to w

anonymous · Answer

write down the complex no into polar form

anonymous · Answer

1/(a+ib) = r e^(i theta)

anonymous · Answer

does it make sense?

anonymous · Answer

hey i tried but i am not getting it.....will u please solve it ???

anonymous · Answer

let me see...

anonymous · Answer

okay...

anonymous · Answer

sorry...it's going to difficult...i thought that it'll be some kind of gaussian integral...but the integrand is like e^{ -i( arc tan(w/a) +arc tan(w/b) ) +i wt }

anonymous · Answer

so need to use complex integral

hartnn · Answer

even wolf gives this: http://www.wolframalpha.com/input/?i=integral+of+%28e%5E%28iwt%29%2F%28%28a%2Biw%29%28b%2Biw%29%29%29&dataset=

anonymous · Answer

........i tried it by  partial  fractions.....but getting stuck ahead...

hartnn · Answer

u have the limits or is this indefinite integration ?

anonymous · Answer

indefinite......

anonymous · Answer

the ans given is very complex...

hartnn · Answer

hmm..maybe @experimentX can help with complex integration.

anonymous · Answer

ill try...

anonymous · Answer

hey but how do i ask experimentx??

hartnn · Answer

i tagged him,he will see this question when he comes online.

anonymous · Answer

okay,......thanks a lot....

experimentx · Answer

what are the limits of your integration?

hartnn · Answer

no limits,its indefinite

experimentx · Answer

I am not sure I can do indefinite integration ... usually complex integration comes with limits. The best thing to do is 
let w = x+iy and dw = dx + idy and integrate with dx and dy ... and see how it goes.

experimentx · Answer

$$ \frac{ 1 }{ a+iw}\times \frac{ 1 }{ b+iw }\times e ^{iwt} = {1 \over b-a} \left( \frac{ 1 }{ a+iw} -  \frac{ 1 }{ b+iw } \right)\times e ^{iwt}$$

this looks like 
$$ {e^{ax} \over b + cx} $$

experimentx · Answer

this type of integration are called Exponential integration and is not closed in elementary functions. http://www.wolframalpha.com/input/?i=integrate+e^%28ax%29%2F%28b%2Bcx%29

experimentx · Answer

probably you are missing limits.

experimentx · Answer

even the improper integrals for above type diverges ... you need something like http://www.wolframalpha.com/input/?i=integrate+e^%28I+*+z%29%2F%285%2B+I+z%29^2+from+-infinity+to+%2Binfinity they have nice value that can be calculated from contour integrals

anonymous · Answer

hey thanks.....i got it.....thanks a lot...

experimentx · Answer

can you share it with us?

experimentx · Answer

really i'm interested in solution ...

anonymous · Answer

okay.....wait...